XY-Chain

Very Hard

A chain of bivalue cells; the common candidate at both ends can be eliminated from cells seeing both ends.

How It Works

A chain formed by bivalue cells connected through shared candidates. The candidate common to both ends of the chain can be eliminated from any cell seeing both endpoints.

This is the generalization of XY-Wing: an XY-Wing is simply a 3-cell XY-Chain. Longer chains are more powerful but harder to find.

Example

35
24
58
6948
23
632457658
293785
49
67
458
28
9657
23
965748
69
57
849574869
5869
57
3786
69
4758
69
475
37
658679
35
8
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Chain: R1C1={3,5}-R1C4={5,8}-R4C4={8,2}-R4C9={2,3}. Common candidate at both ends is 3 → Eliminate 3 from cells seeing both R1C1 and R4C9.

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Hard25 givensStrict